The invention is based on an internal combustion engine fuel injection system that functions with pump nozzles. In a known fuel injection system of this kind, the apparatus for controlling the injection onset is arranged to control the servo fluid for the pump piston drive in proportion with the cycles of the engine and is entirely separate from the fuel metering apparatus that determines the fuel quantity to be injected and stored in a chamber below the pump piston. The two apparatuses have in common solely that they are both driven by the internal combustion engine. Injection systems which operate with pump/nozzles are well known to be relatively expensive both in terms of structure and cost. If injection systems of this kind are to be introduced into mid-size engines mass-produced in high quantities as well, then the system's apparatuses and the manner in which they are embodied must be greatly simplified. On the other hand, the particular advantage of such fuel injection systems is their high adaptability to various engines; in other words, they can favorably be made to perform injection in the particular required manner. It is critically important in this context that the various individual interventions made into the fuel metering, injection onset, duration of fuel supply, and so forth be capable of being performed independently of one another. Despite this consideration, in known fuel injection systems any structural simplifications or changes made in order to spare expense also restrict the required capacity of the system to be initially or subsequently adjusted. The total expenditure for such a system, in this case, is then no longer in proper proportion to the advantages which are attainable with such a system.